The pump action has a total damage potential of 11,760 assuming all pellets hit the body, and unperked. AA12 has 12,000. Headshot multiplier is the same.
People say that the AA12 has a tighter spread, but it only has less recoil (according to Phada's Weapon/Specimen stats, maybe having 2 less pellets affects spread somehow, but the numerical 'spread' value is still the same). And there tends to be a belief that nobody with the default shotgun actually aims for the head - where it really is easier to get headshots with it.
I've also noticed that shotguns sometimes fire AFTER the recoil takes place, or bug out in zed time, which is very noticeable with both of the guns in question, but easier to compensate for with the pump.
Plus with my perk levels at the moment, the AA12 generally takes 2 - 3 shots to down something, where a single shotgun blast will decap bloats, gores, etc with ease. And if I don't kill something behind that nasty 'ol gorefast with one shot, the commando only needs 1 bullet to finish it off.
So yeah. If anybody on my team ever needs money for anything I'm not getting the AA. If there's a huge amount of cash near the end of the game, sure, but whenever I use the AA12 I start to miss my pump action for trash (or the HS).